Let's Start Thinking


Slide Notes

Glossary

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Equation of a Circle

Circles in the World Around You

A circle with the center, diameter, and radius labeled.

Circles in the World Around You Continued

 

Circles in the World Around You Continued

A circle

Area: \(\pi r^2\)

Circumference: \(2\pi r\) or \(\pi d\)

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Lesson Goals

  • Develop the equation for a circle with centre \((0,0)\) and radius \(r\).
  • Given the equation of a circle, identify the radius and draw a sketch.
  • Develop the equation for a circle with centre \((h,k)\) and radius \(r\).
  • Solve problems involving the equation of a circle.

Try This

Shakeel is designing a T-shirt logo, shown here, using computer software. He has programmed the equation of the smaller circle as \(x^2+y^2=9\). Determine the area of the shaded region shown in the logo design.

Note: The small circle is tangent to the midpoints of the square. The large circle passes through the four vertices of the square.

Shakeel's t-shirt design is the circle x squared + y squared = 9, inscribed in a square, which is inscribed in a larger circle. The shaded portion includes the smaller circle, and the portions of the larger circle which don't overlap with the square.